One example of a tool which is used for a cutting operation and has edges on both sides is a grooving tool. FIG. 30 shows the end portion of a conventional grooving tool 31. As is apparent from FIG. 30, the grooving tool has edges on both sides, and the end portions of the edges have the same tip radius r. In cutting a workpiece with the grooving tool 31, a phantom tip point 32 is provided at the end of one of the edges; that is, the cutting operation is carried out with the phantom tip point as a control point. For instance in the case where, as shown in FIG. 31, a final machining configuration 33 is formed with the left phantom tip point 32 as the control point as shown in FIG. 30, first a machining configuration 34 is formed which is obtained by reducing the width of the final configuration as much as the width of the tool, and then the tool 31 is moved along the offset configuration 35 which is formed by adjusting the machining configuration 34 as much as the tip radius of the edge.
For a cutting tool having edges on both sides which are different in tip radius, there has been provided no method of forming an offset configuration which is determined taking the tip radius into account. Therefore, in the case where a work-piece is cut with a machine tool operated under the control of a numerical control device (hereinafter referred to merely as "an NC machine", when applicable), a cutting tool 36 is used which, as shown in FIG. 32, has an edge on one side.
In FIG. 32, reference numeral 13 designates a cylindrical workpiece to be cut; 14, a final machining configuration; 15, a chuck; and 16, the central axis of rotation. The workpiece 13 is cut as follows: While the workpiece 13 is being rotated, the cutting tool 36 is moved in a horizontal direction, or in a Z-axis direction, and in a vertical direction, or in an X-axis direction. In this cutting operation, the final machining configuration is modified into a configuration which can be formed with the tip angle of the cutting tool 36.
A method of forming an offset configuration for the cutting tool 36 will be described with reference to FIG. 33 which is an explanatory diagram. In FIG. 33, line (R0-R1-R2-R3-R4-R5-R6-R7-R8) is the final machining configuration. In forming the configuration 37 with the cutting tool 36 which is obtained by adjusting the line according to the tip angle of the cutting tool 36, the center c3 of the tip radius of the cutting tool is utilized to control the movement of the cutting tool 36. Accordingly, the line (P0-P1-P2-P3-P4-P5-P6-P6-P7-P8-P9-P10) which is obtained by shifting the aforementioned line 37 as much as the tip radius r3 of the cutting tool 36 is the offset configuration which is the locus of the control center of the cutting tool 36.
A method of processing data in forming the offset configuration 38 (P0-P1 . . . P10) to control the cutting tool 36 according to the final machining configuration 14 (R0-R1 . . . R8) will be described with reference to a flow chart shown in FIG. 34.
First, parts (R0-R1-R2) and (R3-R4-R5) of the final machining configuration are modified into configurations (R0-Q0-R2) and (R3-Q1-R5) which can be formed with the tip angle of the cutting tool (Step S31). Then, the point P0 which is vertically away from the start point R0 as much as the tip radius r3 is obtained, and it is employed as a start point block (Step S32). All configuration blocks including the start point (R0) block have a data structure as shown in FIG. 35.
The flag region of the data structure stores data indicating whether or not the block is of the final machining configuration, and data indicating whether it is a start point, or a straight line, or an arc. In the case where the block is a start point, the coordinates of the start point are stored in the X and Z areas; and in the other cases, the coordinates of the final point are stored therein. For instance for the block (R0-Q0), the coordinates of the point Q0 are written therein. When the configuration is an arc, the coordinates of the center of the arc are written in regions CX and CZ, and the radius is written in a region R. The above-described data structure 39 is stored, as a series of blocks 39a through 39n in memory as shown in FIG. 36.
After the data processing of the start point R0, the data processing of the next block 39b is started. In the data processing, first the configuration of the block 39b is detected (Step S33), and it is determined from the flag region whether or not the block is of the final configuration (Step S34). When the block is not of the final configuration, an offset configuration to the final point for the cutting tool is formed (Step S35). For instance in the case of the block 39b indicating the part (R0-Q0), the data block of an offset configuration (P1) which is shifted as much as the tip radius from the point Q0 is formed, and the data block thus formed is written after the offset configuration data block train which has been formed before (Step S36). The above-described operation is successively carried out until the final configuration is obtained. As a result, the data block train of the offset configuration 38 which is the locus of the control center of the cutting tool 36 is formed. Thus the data processing operation has been ended. The movement of the cutting tool 36 is controlled according to the data of the offset configuration data block train thus formed, to form the configuration (R0-Q0 . . . R8) 37.
As was described above, with the conventional NC machine, it is necessary to change the parts (R0-R1-R2) and (R3-R4-R5) of the final machining configuration into (R0-Q0-R2) and (R3-Q1-R5) according to the tip angle of the cutting tool; that is, it is necessary to perform a so-called "tip configuration correction", as a result of which, in FIG. 37, the parts (R0-R1-Q0-R0) and (R3-R4-Q1-R3) are left uncut. The parts thus left uncut must be cut with another cutting tool. Accordingly, it takes labor and time to calculate the configurations of the parts, and to cut the parts.
In the above-described method, the offset configuration is determined based on the one tip radius of the cutting tool 36. Therefore, the method is not applicable to the formation of an offset configuration for controlling the position of the offset tool which has two nose radii and cuts with both sides, and accordingly the NC machine cannot use a cutting tool having edges on both sides; that is, it cannot machine a workpiece with high efficiency.